Vector random variables: expected values of random vectors and matrices; covariance matrices; linear transforms of random vectors; further properties of the covariance matrix; singular and non-singular distributions; quadratic functions of random vectors. Distribution concepts: distribution of a random vector; multivariate moment generating functions. Transformation of random variables: vector transformation and Jacobian; change of variables in multiple integrals; distribution of functions of random vectors; some applications – the Beta-distribution family; the Chi-square, t – and  F – distributions. Order statistics: order transformation; joint distributions of order statistics; marginal distributions; alternative methods.  Multivariate normal distribution: definition and examples; singular and non-singular distributions; properties of the multivariate normal distribution; multivariate normal density; independence of multivariate normal vectors. Conditional distribution: